

////////////////////////////////////////////////
// Get the local conditions on a ternary form //
////////////////////////////////////////////////
void FindTernaryLocalConditions_New(long Q[6], vector<long> & local_mod_vector,
				    long local_repn_array[][9], vector<long> & aniso_vector) { 


  // WARNING:  This only works when the number of level primes is <= the number of rows in local_repn_array...   

/*
void FindTernaryLocalConditions(long local_array[][9], long Q[6],   
vector<long> & prime_list) { 
*/

  // NOTATION: 
  // =========
  // The structure of the local array is given by:
  //         [ p, *, *, *, *, 0, 0, 0, 0]  for p>2
  //   where the * is a number saying the smallest power k so that the
  //   number (p^2k * x) in the squareclass x is represented.  When
  //   p>2 this is given by x = 1, r, p, p*r.  When p=2 this is given
  //   by x = ..... .


  // Functions needed:
  //   ord(x, p)
  //   QFlevel(Q) -- long QF_Ternary_Level(long[6])
  

  // Make a Matrix_mpz for the ternary form 
  // (this by convention will be the matrix of 2Q for integrality reasons)
  Matrix_mpz QQ;
  QQ.SetDims(3,3);
  QQ(1,1) = 2 * Q[0];
  QQ(1,2) = Q[1];
  QQ(2,1) = Q[1];
  QQ(1,3) = Q[2];
  QQ(3,1) = Q[2];
  QQ(2,2) = 2 * Q[3];
  QQ(2,3) = Q[4];
  QQ(3,2) = Q[4];
  QQ(3,3) = 2 * Q[5];

  cout << " QQ is given by: " << endl;
  cout << QQ << endl;

  // Find the level
  //      long N = QF_Ternary_Level(Q); 
  mpz_class NN = QQ.QFLevel();
  long N;
  N = NN.get_ui();


  // Make a list of primes
  long primelist[1000] = { 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37,
  41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107,
  109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179,
  181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251,
  257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331,
  337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409,
  419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487,
  491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577,
  587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653,
  659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743,
  751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829,
  839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929,
  937, 941, 947, 953, 967, 971, 977, 983, 991, 997, 1009, 1013, 1019,
  1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091,
  1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171,
  1181, 1187, 1193, 1201, 1213, 1217, 1223, 1229, 1231, 1237, 1249,
  1259, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307, 1319,
  1321, 1327, 1361, 1367, 1373, 1381, 1399, 1409, 1423, 1427, 1429,
  1433, 1439, 1447, 1451, 1453, 1459, 1471, 1481, 1483, 1487, 1489,
  1493, 1499, 1511, 1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571,
  1579, 1583, 1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637,
  1657, 1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733,
  1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, 1823,
  1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1901, 1907,
  1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987, 1993, 1997, 1999,
  2003, 2011, 2017, 2027, 2029, 2039, 2053, 2063, 2069, 2081, 2083,
  2087, 2089, 2099, 2111, 2113, 2129, 2131, 2137, 2141, 2143, 2153,
  2161, 2179, 2203, 2207, 2213, 2221, 2237, 2239, 2243, 2251, 2267,
  2269, 2273, 2281, 2287, 2293, 2297, 2309, 2311, 2333, 2339, 2341,
  2347, 2351, 2357, 2371, 2377, 2381, 2383, 2389, 2393, 2399, 2411,
  2417, 2423, 2437, 2441, 2447, 2459, 2467, 2473, 2477, 2503, 2521,
  2531, 2539, 2543, 2549, 2551, 2557, 2579, 2591, 2593, 2609, 2617,
  2621, 2633, 2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687, 2689,
  2693, 2699, 2707, 2711, 2713, 2719, 2729, 2731, 2741, 2749, 2753,
  2767, 2777, 2789, 2791, 2797, 2801, 2803, 2819, 2833, 2837, 2843,
  2851, 2857, 2861, 2879, 2887, 2897, 2903, 2909, 2917, 2927, 2939,
  2953, 2957, 2963, 2969, 2971, 2999, 3001, 3011, 3019, 3023, 3037,
  3041, 3049, 3061, 3067, 3079, 3083, 3089, 3109, 3119, 3121, 3137,
  3163, 3167, 3169, 3181, 3187, 3191, 3203, 3209, 3217, 3221, 3229,
  3251, 3253, 3257, 3259, 3271, 3299, 3301, 3307, 3313, 3319, 3323,
  3329, 3331, 3343, 3347, 3359, 3361, 3371, 3373, 3389, 3391, 3407,
  3413, 3433, 3449, 3457, 3461, 3463, 3467, 3469, 3491, 3499, 3511,
  3517, 3527, 3529, 3533, 3539, 3541, 3547, 3557, 3559, 3571, 3581,
  3583, 3593, 3607, 3613, 3617, 3623, 3631, 3637, 3643, 3659, 3671,
  3673, 3677, 3691, 3697, 3701, 3709, 3719, 3727, 3733, 3739, 3761,
  3767, 3769, 3779, 3793, 3797, 3803, 3821, 3823, 3833, 3847, 3851,
  3853, 3863, 3877, 3881, 3889, 3907, 3911, 3917, 3919, 3923, 3929,
  3931, 3943, 3947, 3967, 3989, 4001, 4003, 4007, 4013, 4019, 4021,
  4027, 4049, 4051, 4057, 4073, 4079, 4091, 4093, 4099, 4111, 4127,
  4129, 4133, 4139, 4153, 4157, 4159, 4177, 4201, 4211, 4217, 4219,
  4229, 4231, 4241, 4243, 4253, 4259, 4261, 4271, 4273, 4283, 4289,
  4297, 4327, 4337, 4339, 4349, 4357, 4363, 4373, 4391, 4397, 4409,
  4421, 4423, 4441, 4447, 4451, 4457, 4463, 4481, 4483, 4493, 4507,
  4513, 4517, 4519, 4523, 4547, 4549, 4561, 4567, 4583, 4591, 4597,
  4603, 4621, 4637, 4639, 4643, 4649, 4651, 4657, 4663, 4673, 4679,
  4691, 4703, 4721, 4723, 4729, 4733, 4751, 4759, 4783, 4787, 4789,
  4793, 4799, 4801, 4813, 4817, 4831, 4861, 4871, 4877, 4889, 4903,
  4909, 4919, 4931, 4933, 4937, 4943, 4951, 4957, 4967, 4969, 4973,
  4987, 4993, 4999, 5003, 5009, 5011, 5021, 5023, 5039, 5051, 5059,
  5077, 5081, 5087, 5099, 5101, 5107, 5113, 5119, 5147, 5153, 5167,
  5171, 5179, 5189, 5197, 5209, 5227, 5231, 5233, 5237, 5261, 5273,
  5279, 5281, 5297, 5303, 5309, 5323, 5333, 5347, 5351, 5381, 5387,
  5393, 5399, 5407, 5413, 5417, 5419, 5431, 5437, 5441, 5443, 5449,
  5471, 5477, 5479, 5483, 5501, 5503, 5507, 5519, 5521, 5527, 5531,
  5557, 5563, 5569, 5573, 5581, 5591, 5623, 5639, 5641, 5647, 5651,
  5653, 5657, 5659, 5669, 5683, 5689, 5693, 5701, 5711, 5717, 5737,
  5741, 5743, 5749, 5779, 5783, 5791, 5801, 5807, 5813, 5821, 5827,
  5839, 5843, 5849, 5851, 5857, 5861, 5867, 5869, 5879, 5881, 5897,
  5903, 5923, 5927, 5939, 5953, 5981, 5987, 6007, 6011, 6029, 6037,
  6043, 6047, 6053, 6067, 6073, 6079, 6089, 6091, 6101, 6113, 6121,
  6131, 6133, 6143, 6151, 6163, 6173, 6197, 6199, 6203, 6211, 6217,
  6221, 6229, 6247, 6257, 6263, 6269, 6271, 6277, 6287, 6299, 6301,
  6311, 6317, 6323, 6329, 6337, 6343, 6353, 6359, 6361, 6367, 6373,
  6379, 6389, 6397, 6421, 6427, 6449, 6451, 6469, 6473, 6481, 6491,
  6521, 6529, 6547, 6551, 6553, 6563, 6569, 6571, 6577, 6581, 6599,
  6607, 6619, 6637, 6653, 6659, 6661, 6673, 6679, 6689, 6691, 6701,
  6703, 6709, 6719, 6733, 6737, 6761, 6763, 6779, 6781, 6791, 6793,
  6803, 6823, 6827, 6829, 6833, 6841, 6857, 6863, 6869, 6871, 6883,
  6899, 6907, 6911, 6917, 6947, 6949, 6959, 6961, 6967, 6971, 6977,
  6983, 6991, 6997, 7001, 7013, 7019, 7027, 7039, 7043, 7057, 7069,
  7079, 7103, 7109, 7121, 7127, 7129, 7151, 7159, 7177, 7187, 7193,
  7207, 7211, 7213, 7219, 7229, 7237, 7243, 7247, 7253, 7283, 7297,
  7307, 7309, 7321, 7331, 7333, 7349, 7351, 7369, 7393, 7411, 7417,
  7433, 7451, 7457, 7459, 7477, 7481, 7487, 7489, 7499, 7507, 7517,
  7523, 7529, 7537, 7541, 7547, 7549, 7559, 7561, 7573, 7577, 7583,
  7589, 7591, 7603, 7607, 7621, 7639, 7643, 7649, 7669, 7673, 7681,
  7687, 7691, 7699, 7703, 7717, 7723, 7727, 7741, 7753, 7757, 7759,
  7789, 7793, 7817, 7823, 7829, 7841, 7853, 7867, 7873, 7877, 7879,
  7883, 7901, 7907, 7919};
  
  // Find the number of primes dividing the level long Num_Primes;
  long Num_Primes = 0;
  long ind = 0;
  while (primelist[ind] <= (2*N)){
    if ((2*N) % primelist[ind] == 0) 
      Num_Primes++;
    ind++;
  }
  
  // Make a vector of primes dividing 2*N
  long ct = 0;
  ind = 0;
  long level_primes[Num_Primes];
  while (ct < Num_Primes){
    if ((2*N) % primelist[ind] == 0) {
      level_primes[ct] = primelist[ind];
      ct++;
    }
    ind++;
  }
  

  // Find the modulus for each prime 
  long repn_mods[Num_Primes];
  for (long i=0; i<Num_Primes; i++)
    repn_mods[i] = LongPow(level_primes[i], Valuation(4*N, level_primes[i]) + 2);
 


  cout << "N = " << N << endl;
  cout << "Valuation(16, 2) = " << Valuation(16, 2) << endl;
  for (long i=0; i<Num_Primes; i++)
    cout << " i = " << i << "   level prime = " << level_primes[i] 
	 << "   repn_mod = " << repn_mods[i] << endl;


  // Make a table of local normal forms of QQ at each prime p | N
  Matrix_mpz local_normal_forms[Num_Primes];
  for (long i=0; i < Num_Primes; i++)
    local_normal_forms[i] = LocalNormal(QQ, mpz_class(level_primes[i]));

  /*
  // Make the representation array
    long repn_array[Num_Primes][9];
  */


  /*
  // DIAGNOSTIC
  cout << " Here is the uninitialized array " << endl;
  cout << " These are the local representability conditions (array): " << endl;
  for (long i=0; i < Num_Primes; i++) {
    for (long j=0; j < 9; j++)
      cout << local_repn_array[i][j] << ", ";
    cout << endl;
  }
  cout << endl;
  */


  // Check local representability for each prime
  for (long i=0; i<Num_Primes; i++) {
    long p = level_primes[i];
    local_repn_array[i][0] = p;
    
    // Make the squareclass vector
    long sqclass_size;
    if (p == 2) 
      sqclass_size = 8;
    else 
      sqclass_size = 4;

    long sqclass[sqclass_size];

    if (p == 2) {
      sqclass[0] = 1;
      sqclass[1] = 3;
      sqclass[2] = 5;
      sqclass[3] = 7;
      sqclass[4] = 2;
      sqclass[5] = 6;
      sqclass[6] = 10;
      sqclass[7] = 14;
    }
    else {
      long r = NonResidue(mpz_class(p)).get_ui();
      sqclass[0] = 1;
      sqclass[1] = r;
      sqclass[2] = p;
      sqclass[3] = p*r;
    }

    // Check the representability in each squareclass
    for (long j=0; j<sqclass_size; j++) {
      long m = sqclass[j];
      long k = 0;
      bool repn_flag = false;
      //      cout << "hi -- Using p = " << level_primes[i] << " and 4*N = " << (4*N) << endl;
      long prime_pow = Valuation(4*N, level_primes[i]) + 2;  // The power of the repn modulus
      //      cout << "bye" << endl;
      while ((repn_flag == false) && (k < prime_pow)) {  // NOTE: This can be made smaller by (approximately) a factor of 2...
	if (Local_Density(local_normal_forms[i], mpz_class(p), mpz_class(m)) > 0) {
	  local_repn_array[i][j+1] = k;
	  repn_flag = true;
	}
	k++;
	m = m * p * p;
      }
      
      // If we're not represented, write a negative number
      // to signify we checked up to x * p^(2*k).
      if (repn_flag == false)
	local_repn_array[i][j+1] = -(k - 1);
      
    }
  }

  /*
  // DIAGNOSTIC
  cout << " Here is the initialized array " << endl;
  cout << " These are the local representability conditions (array): " << endl;
  for (long i=0; i < Num_Primes; i++) {
    for (long j=0; j < 9; j++)
      cout << local_repn_array[i][j] << ", ";
    cout << endl;
  }
  cout << endl;
  */

      
  // Make the big modulus
  long Bigmod = 1;
  for (long i=0; i < Num_Primes; i++)
    Bigmod = Bigmod * repn_mods[i];


  // Return the modulus and list of local failures
  //       local_repn_array = repn_array;
  
  local_mod_vector.clear();
  for(long j=0; j<Num_Primes; j++)
    local_mod_vector.push_back(repn_mods[j]);

  /*
  // DIAGNOSTIC
  for(long j=0; j<Num_Primes; j++)
    cout << "Primelist[" << j << "] = " << primelist[j] << endl;
  */

  //   cout << "\n\n Making Aniso Primes \n\n";

  aniso_vector.clear();
  for(long j=0; j<Num_Primes; j++)
    if (IsAnisotropic(QQ, mpz_class(level_primes[j])) == true) {
      aniso_vector.push_back(level_primes[j]);
      //      cout << " Found an anisotropic prime: " << level_primes[j] << endl;
    }
  //   cout << "\n\n Finished Making Aniso Primes \n\n";
}





//////////////////////////////////////////////////
// Get the local conditions on a quadratic form //
//////////////////////////////////////////////////
void FindLocalConditions(Matrix_mpz QQ, vector<long> & local_mod_vector,
				    long local_repn_array[][9], vector<long> & aniso_vector) { 


  // WARNING:  This only works when the number of level primes is <= the number of rows in local_repn_array...   

/*
void FindTernaryLocalConditions(long local_array[][9], long Q[6],   
vector<long> & prime_list) { 
*/

  // NOTATION: 
  // =========
  // The structure of the local array is given by:
  //         [ p, *, *, *, *, 0, 0, 0, 0]  for p>2
  //   where the * is a number saying the smallest power k so that the
  //   number (p^2k * x) in the squareclass x is represented.  When
  //   p>2 this is given by x = 1, r, p, p*r.  When p=2 this is given
  //   by x = ..... .


  // Functions needed:
  //   ord(x, p)
  //   QFlevel(Q) -- long QF_Ternary_Level(long[6])
  

  // Show the matrix QQ
  // (By convention QQ will be the matrix of 2Q for integrality reasons)
  /*
  cout << " QQ is given by: " << endl;
  cout << QQ << endl;
  */


  // Find the level
  //      long N = QF_Ternary_Level(Q); 
  mpz_class NN = QQ.QFLevel();
  long N;
  N = NN.get_ui();


  /*
  // Remove any overall scaling factor (to ensure QQ is primitive)
  mpz_class scaling_factor = 1;
  for(i=1; i<QQ.NumRows(); i++)
    for(j=i; j<QQ.NumRows(); j++)
      if (i==j)
	scaling_factor = GCD(scaling_factor, QQ(i,i));
      else
	scaling_factor = GCD(2*scaling_factor, QQ(i,i));
  */


  // Make a list of primes
  long primelist[1000] = { 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37,
  41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107,
  109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179,
  181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251,
  257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331,
  337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409,
  419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487,
  491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577,
  587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653,
  659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743,
  751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829,
  839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929,
  937, 941, 947, 953, 967, 971, 977, 983, 991, 997, 1009, 1013, 1019,
  1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091,
  1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171,
  1181, 1187, 1193, 1201, 1213, 1217, 1223, 1229, 1231, 1237, 1249,
  1259, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307, 1319,
  1321, 1327, 1361, 1367, 1373, 1381, 1399, 1409, 1423, 1427, 1429,
  1433, 1439, 1447, 1451, 1453, 1459, 1471, 1481, 1483, 1487, 1489,
  1493, 1499, 1511, 1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571,
  1579, 1583, 1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637,
  1657, 1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733,
  1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, 1823,
  1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1901, 1907,
  1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987, 1993, 1997, 1999,
  2003, 2011, 2017, 2027, 2029, 2039, 2053, 2063, 2069, 2081, 2083,
  2087, 2089, 2099, 2111, 2113, 2129, 2131, 2137, 2141, 2143, 2153,
  2161, 2179, 2203, 2207, 2213, 2221, 2237, 2239, 2243, 2251, 2267,
  2269, 2273, 2281, 2287, 2293, 2297, 2309, 2311, 2333, 2339, 2341,
  2347, 2351, 2357, 2371, 2377, 2381, 2383, 2389, 2393, 2399, 2411,
  2417, 2423, 2437, 2441, 2447, 2459, 2467, 2473, 2477, 2503, 2521,
  2531, 2539, 2543, 2549, 2551, 2557, 2579, 2591, 2593, 2609, 2617,
  2621, 2633, 2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687, 2689,
  2693, 2699, 2707, 2711, 2713, 2719, 2729, 2731, 2741, 2749, 2753,
  2767, 2777, 2789, 2791, 2797, 2801, 2803, 2819, 2833, 2837, 2843,
  2851, 2857, 2861, 2879, 2887, 2897, 2903, 2909, 2917, 2927, 2939,
  2953, 2957, 2963, 2969, 2971, 2999, 3001, 3011, 3019, 3023, 3037,
  3041, 3049, 3061, 3067, 3079, 3083, 3089, 3109, 3119, 3121, 3137,
  3163, 3167, 3169, 3181, 3187, 3191, 3203, 3209, 3217, 3221, 3229,
  3251, 3253, 3257, 3259, 3271, 3299, 3301, 3307, 3313, 3319, 3323,
  3329, 3331, 3343, 3347, 3359, 3361, 3371, 3373, 3389, 3391, 3407,
  3413, 3433, 3449, 3457, 3461, 3463, 3467, 3469, 3491, 3499, 3511,
  3517, 3527, 3529, 3533, 3539, 3541, 3547, 3557, 3559, 3571, 3581,
  3583, 3593, 3607, 3613, 3617, 3623, 3631, 3637, 3643, 3659, 3671,
  3673, 3677, 3691, 3697, 3701, 3709, 3719, 3727, 3733, 3739, 3761,
  3767, 3769, 3779, 3793, 3797, 3803, 3821, 3823, 3833, 3847, 3851,
  3853, 3863, 3877, 3881, 3889, 3907, 3911, 3917, 3919, 3923, 3929,
  3931, 3943, 3947, 3967, 3989, 4001, 4003, 4007, 4013, 4019, 4021,
  4027, 4049, 4051, 4057, 4073, 4079, 4091, 4093, 4099, 4111, 4127,
  4129, 4133, 4139, 4153, 4157, 4159, 4177, 4201, 4211, 4217, 4219,
  4229, 4231, 4241, 4243, 4253, 4259, 4261, 4271, 4273, 4283, 4289,
  4297, 4327, 4337, 4339, 4349, 4357, 4363, 4373, 4391, 4397, 4409,
  4421, 4423, 4441, 4447, 4451, 4457, 4463, 4481, 4483, 4493, 4507,
  4513, 4517, 4519, 4523, 4547, 4549, 4561, 4567, 4583, 4591, 4597,
  4603, 4621, 4637, 4639, 4643, 4649, 4651, 4657, 4663, 4673, 4679,
  4691, 4703, 4721, 4723, 4729, 4733, 4751, 4759, 4783, 4787, 4789,
  4793, 4799, 4801, 4813, 4817, 4831, 4861, 4871, 4877, 4889, 4903,
  4909, 4919, 4931, 4933, 4937, 4943, 4951, 4957, 4967, 4969, 4973,
  4987, 4993, 4999, 5003, 5009, 5011, 5021, 5023, 5039, 5051, 5059,
  5077, 5081, 5087, 5099, 5101, 5107, 5113, 5119, 5147, 5153, 5167,
  5171, 5179, 5189, 5197, 5209, 5227, 5231, 5233, 5237, 5261, 5273,
  5279, 5281, 5297, 5303, 5309, 5323, 5333, 5347, 5351, 5381, 5387,
  5393, 5399, 5407, 5413, 5417, 5419, 5431, 5437, 5441, 5443, 5449,
  5471, 5477, 5479, 5483, 5501, 5503, 5507, 5519, 5521, 5527, 5531,
  5557, 5563, 5569, 5573, 5581, 5591, 5623, 5639, 5641, 5647, 5651,
  5653, 5657, 5659, 5669, 5683, 5689, 5693, 5701, 5711, 5717, 5737,
  5741, 5743, 5749, 5779, 5783, 5791, 5801, 5807, 5813, 5821, 5827,
  5839, 5843, 5849, 5851, 5857, 5861, 5867, 5869, 5879, 5881, 5897,
  5903, 5923, 5927, 5939, 5953, 5981, 5987, 6007, 6011, 6029, 6037,
  6043, 6047, 6053, 6067, 6073, 6079, 6089, 6091, 6101, 6113, 6121,
  6131, 6133, 6143, 6151, 6163, 6173, 6197, 6199, 6203, 6211, 6217,
  6221, 6229, 6247, 6257, 6263, 6269, 6271, 6277, 6287, 6299, 6301,
  6311, 6317, 6323, 6329, 6337, 6343, 6353, 6359, 6361, 6367, 6373,
  6379, 6389, 6397, 6421, 6427, 6449, 6451, 6469, 6473, 6481, 6491,
  6521, 6529, 6547, 6551, 6553, 6563, 6569, 6571, 6577, 6581, 6599,
  6607, 6619, 6637, 6653, 6659, 6661, 6673, 6679, 6689, 6691, 6701,
  6703, 6709, 6719, 6733, 6737, 6761, 6763, 6779, 6781, 6791, 6793,
  6803, 6823, 6827, 6829, 6833, 6841, 6857, 6863, 6869, 6871, 6883,
  6899, 6907, 6911, 6917, 6947, 6949, 6959, 6961, 6967, 6971, 6977,
  6983, 6991, 6997, 7001, 7013, 7019, 7027, 7039, 7043, 7057, 7069,
  7079, 7103, 7109, 7121, 7127, 7129, 7151, 7159, 7177, 7187, 7193,
  7207, 7211, 7213, 7219, 7229, 7237, 7243, 7247, 7253, 7283, 7297,
  7307, 7309, 7321, 7331, 7333, 7349, 7351, 7369, 7393, 7411, 7417,
  7433, 7451, 7457, 7459, 7477, 7481, 7487, 7489, 7499, 7507, 7517,
  7523, 7529, 7537, 7541, 7547, 7549, 7559, 7561, 7573, 7577, 7583,
  7589, 7591, 7603, 7607, 7621, 7639, 7643, 7649, 7669, 7673, 7681,
  7687, 7691, 7699, 7703, 7717, 7723, 7727, 7741, 7753, 7757, 7759,
  7789, 7793, 7817, 7823, 7829, 7841, 7853, 7867, 7873, 7877, 7879,
  7883, 7901, 7907, 7919};
  
  // Find the number of primes dividing the level long Num_Primes;
  long Num_Primes = 0;
  long ind = 0;
  while (primelist[ind] <= (2*N)){
    if ((2*N) % primelist[ind] == 0) 
      Num_Primes++;
    ind++;
  }
  
  // Make a vector of primes dividing 2*N
  long ct = 0;
  ind = 0;
  long level_primes[Num_Primes];
  while (ct < Num_Primes){
    if ((2*N) % primelist[ind] == 0) {
      level_primes[ct] = primelist[ind];
      ct++;
    }
    ind++;
  }
  

  // Find the modulus for each prime 
  long repn_mods[Num_Primes];
  for (long i=0; i<Num_Primes; i++)
    repn_mods[i] = LongPow(level_primes[i], Valuation(4*N, level_primes[i]) + 2);
 


  cout << "N = " << N << endl;
  //  cout << "Valuation(16, 2) = " << Valuation(16, 2) << endl;
  for (long i=0; i<Num_Primes; i++)
    cout << " i = " << i << "   level prime = " << level_primes[i] 
	 << "   repn_mod = " << repn_mods[i] << endl;


  // Make a table of local normal forms of QQ at each prime p | N
  Matrix_mpz local_normal_forms[Num_Primes];
  for (long i=0; i < Num_Primes; i++)
    local_normal_forms[i] = LocalNormal(QQ, mpz_class(level_primes[i]));

  /*
  // Make the representation array
    long repn_array[Num_Primes][9];
  */


  /*
  // DIAGNOSTIC
  cout << " Here is the uninitialized array " << endl;
  cout << " These are the local representability conditions (array): " << endl;
  for (long i=0; i < Num_Primes; i++) {
    for (long j=0; j < 9; j++)
      cout << local_repn_array[i][j] << ", ";
    cout << endl;
  }
  cout << endl;
  */


  // Check local representability for each prime
  for (long i=0; i<Num_Primes; i++) {
    long p = level_primes[i];
    local_repn_array[i][0] = p;
    
    // Make the squareclass vector
    long sqclass_size;
    if (p == 2) 
      sqclass_size = 8;
    else 
      sqclass_size = 4;

    long sqclass[sqclass_size];

    if (p == 2) {
      sqclass[0] = 1;
      sqclass[1] = 3;
      sqclass[2] = 5;
      sqclass[3] = 7;
      sqclass[4] = 2;
      sqclass[5] = 6;
      sqclass[6] = 10;
      sqclass[7] = 14;
    }
    else {
      long r = NonResidue(mpz_class(p)).get_ui();
      sqclass[0] = 1;
      sqclass[1] = r;
      sqclass[2] = p;
      sqclass[3] = p*r;
    }

    // Check the representability in each squareclass
    for (long j=0; j<sqclass_size; j++) {
      long m = sqclass[j];
      long k = 0;
      bool repn_flag = false;
      //      cout << "hi -- Using p = " << level_primes[i] << " and 4*N = " << (4*N) << endl;
      long prime_pow = Valuation(4*N, level_primes[i]) + 2;  // The power of the repn modulus
      //      cout << "bye" << endl;
      while ((repn_flag == false) && (k < prime_pow)) {  // NOTE: This can be made smaller by (approximately) a factor of 2...
	if (Local_Density(local_normal_forms[i], mpz_class(p), mpz_class(m)) > 0) {
	  local_repn_array[i][j+1] = k;
	  repn_flag = true;
	}
	k++;
	m = m * p * p;
      }
      
      // If we're not represented, write a negative number
      // to signify we checked up to x * p^(2*k).
      if (repn_flag == false)
	local_repn_array[i][j+1] = -(k - 1);
      
    }
  }

  /*
  // DIAGNOSTIC
  cout << " Here is the initialized array " << endl;
  cout << " These are the local representability conditions (array): " << endl;
  for (long i=0; i < Num_Primes; i++) {
    for (long j=0; j < 9; j++)
      cout << local_repn_array[i][j] << ", ";
    cout << endl;
  }
  cout << endl;
  */

      
  // Make the big modulus
  long Bigmod = 1;
  for (long i=0; i < Num_Primes; i++)
    Bigmod = Bigmod * repn_mods[i];


  // Return the modulus and list of local failures
  //       local_repn_array = repn_array;
  
  local_mod_vector.clear();
  for(long j=0; j<Num_Primes; j++)
    local_mod_vector.push_back(repn_mods[j]);

  /*
  // DIAGNOSTIC
  for(long j=0; j<Num_Primes; j++)
    cout << "Primelist[" << j << "] = " << primelist[j] << endl;
  */

  //   cout << "\n\n Making Aniso Primes \n\n";

  aniso_vector.clear();
  for(long j=0; j<Num_Primes; j++)
    if (IsAnisotropic(QQ, mpz_class(level_primes[j])) == true) {
      aniso_vector.push_back(level_primes[j]);
      //      cout << " Found an anisotropic prime: " << level_primes[j] << endl;
    }
  //   cout << "\n\n Finished Making Aniso Primes \n\n";
}

